Let m=(313)4 and n=(322)4. Find the base 4 expansion of m+n.
(A) (635)4
(B) (32312)4
(C) (21323)4
(D) (1301)4
Answer: (D)
Explanation: We have m=(313)4 and n=(322)4 convert m and n into decimal:
m = 3*42 + 1*41 + 3*40 m = 48 + 4 + 3 m = 55. Now n=3*42 + 2*41 +2*40 n = 48 + 8 +2 n = 58. m + n = 55 + 58 m + n = 113
Now we have to convert 113 in to base 4:
ie step 1-113 % 4 = 1 113 / 4 = 28 step 2- 28 % 4 = 0 28 / 4 = 7 step 3- 7 % 4 = 3 7 / 4 = 1 step 4- 1 % 4 = 1 1 / 4 --> will not divide it in quant. So we have to stop here.
The answer will be Residue from step 4 to step 1 inorder ie 1301
Ans-(1301)4
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